1.2 Gravity As We Know It

summary

Newton’s theory of gravity

Newton understood gravity as a force between two objects that is proportional to their masses ($M$ and $m$) and the inverse of the distance ($r$) between them according to the equation:
$$F = \frac{GMm}{r^2}$$
In Newton’s view, objects move in straight lines through space until the force of gravity from other objects acts on them. However, there are two problems with this picture.
The first is that there is no clear way for two objects to act on one another from a distance. Newton called the idea of an instantaneous, invisible force of gravity “repugnant”, but it was the best he could do at the time.
The second problem is that space itself is ill-defined in Newtonian gravity. It is essentially the box in which all things exist and move about, but Newton never actually described it in any detail.
Absolute empty space is a very Newtonian idea.

The situation changed dramatically in the 19th century.

Faraday and Maxwell, while working on demystifying electric forces, realized that there is another ingredient in the world: the electromagnetic field.
The electromagnetic field is thought to be present throughout the universe. It is the substrate through which two charges, separated by distance, could indirectly influence each other.
Charged particles affect the field, which in turn affects the behavior of charged particles. The information of the charges (sign of the charge, strength of the charge) travels through the field.
According to Maxwell, the electric field could oscillate at different frequencies, producing not only visible light but also new forms of radiation like radio waves.

Einstein applied Maxwell’s ideas about electromagnetism to gravity.

Einstein realized that a ubiquitous field that can transmit information and influence particles, like the electromagnetic field, could also solve the problems with Newton’s gravity.
Rather than try to come up with an entirely new gravitational field, Einstein saw that the field was already there – it was Newton’s space. But rather than conceive of space as a rigid container as Newton did, Einstein realized it can bend and curve, just like Maxwell’s electromagnetic field could oscillate.
Einstein reformulated three-dimensional space as four-dimensional spacetime, forming a cohesive geometric framework that treats time as another dimension of his new gravitational field.
Einstein published his general theory of relativity in November 1915. The concept of a gravitational field that is influenced by (and in turn influences) matter is essentially captured by a single equation which relates the curvature of the field ($R$) to the matter within it ($T$): $$R_{ab}- \frac{1}{2}g_{ab}R = T_{ab}$$

Einstein’s spacetime has some unusual consequences.

One of the biggest consequences of general relativity is that it abolished the force of gravity. In the new framework, the effects of gravity are the result of a curved spacetime that alters the motion of matter.
When you throw a ball into the air, it does not continue traveling up in a straight line but falls back down. While the simplest explanation of such behavior would be to say that a force acted upon it, the reality is that the curvature of spacetime changes what a straight line is.
The path of a ball thrown into the air is a geodesic, which is the equivalent of a straight line in a curved four-dimensional spacetime. An example of a geodesic is the route of airplanes traveling between the US and Europe – they go north and then south instead of straight east-west because that is actually the shortest path on a globe.
Another peculiar consequence of general relativity is that time passes more slowly in regions of high spacetime curvature. This has been experimentally demonstrated over distances as small as 30 centimeters.
One of general relativity’s most famous consequences results from intense curvatures in spacetime that form singularities. Black holes occur when spacetime curvature is such that nothing can escape, not even light.